Noncommutative Integration and Symmetry Algebra of the Dirac Equation on the Lie Groups
- 18 Downloads
The algebra of first-order symmetry operators of the Dirac equation on four-dimensional Lie groups with right-invariant metric is investigated. It is shown that the algebra of symmetry operators is in general not a Lie algebra. Noncommutative reduction mediated by spin symmetry operators is investigated. For the Dirac equation on the Lie group SO(2,1) a parametric family of particular solutions obtained by the method of noncommutative integration over a subalgebra containing a spin symmetry operator is constructed.
KeywordsDirac equation noncommutative integration symmetry algebra
Unable to display preview. Download preview PDF.
- 3.V. G. Bagrov and G. F. Karavaev, Exact Solutions of Relativistic Wave Equations [in Russian], Nauka, Novosibirsk (1982).Google Scholar
- 5.V. V. Obukhov, The Steckel Spaces in Gravitation Theory [in Russian], Tomsk State Pedagogical University Publishing House, Tomsk (2006).Google Scholar
- 6.V. N. Shapovalov and G. G. Ékle, Algebraic Properties of the Dirac Equation [in Russian], Kalmyk University Publishing House, Élista (1972).Google Scholar
- 8.V. N. Shapovalov and I. V. Shirokov, Teor. Mat. Fiz., 106, No. 3–15 (1996).Google Scholar
- 14.R. G. McLenaghan and Ph. Spindel, Bull. Soc. Math. Belgique, XXXI, 65 (1979).Google Scholar